Make the Cake:

1. Preheat the oven to 350°F (175°C). Grease and line two 8-inch round cake pans.
2. In a skillet, melt 3 tbsp of butter over medium-high heat. Add chopped pecans and toast for 3-4 minutes until fragrant. Set aside to cool.
3. In a large bowl, whisk together the cake flour, granulated sugar, brown sugar, baking powder, baking soda, and salt.
4. Add buttermilk, milk, vanilla extract, vegetable oil, and eggs to the dry ingredients. Mix with a hand or stand mixer until fully combined. Fold in the toasted pecans.
5. Divide the batter evenly between the prepared pans. Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean. Allow cakes to cool completely before frosting.

Make the Frosting:

1. Heat 1 cup of butter in a pan over medium-high heat, stirring constantly, until it turns golden brown and develops a nutty aroma. Transfer to a heat-proof bowl and let cool completely.
2. In a mixer, beat the softened cream cheese until smooth. Add the cooled browned butter and mix until combined.
3. Gradually add the powdered sugar on low speed until incorporated. Increase the speed and beat until fluffy. Add vanilla extract and beat for 3 minutes on medium-high until light and creamy.

Assemble the Cake:

1. Place one cake layer on a serving plate. Spread a thick layer of frosting on top.
2. Add the second cake layer and frost the top and sides.
3. Decorate with toasted pecans for a festive finish.